I don't know if this is really an answer, but I've had a Coleman 6 person spa in service for about 25 years. Yes, 25 years! I have never had the same problems you are experiencing. We learned early on that any clothing (bathing suits etc) must be very clean and rinsed extremely well before going into the spa. Clothes cleaning detergents left in the fabrics release into the pool water and cause foam quickly. The clarifier is good at flocking these soaps, but they do tend to gum up the works quickly. We never lost a lot of pressure however, just had to clean the filter. We also made a habit of completely changing the water at least twice a year. After draining as much as we could via the drain hose, we used a wet vac to get as much out of any low spots. We then put in just enough water to cover the intake close to the bottom and jogged the pump to cycle clean water through the system and get the dirty water out. Again, drain and vacuum and repeat this process until the water looks clear. We do this with the filter out. This will clean out a lot of crap. About once a year just before we do a drain and complete cleaning, we treat the tub with anti-scale cleanser. This cleans the internal pipes of built up scale and solids. In your case, you may want to do this anti-scale treatment for a few days with the circulator on low and the filter out to purge the internal system. Then go ahead and change the water.
Another test you can do is to see how well the pump pushes water. When you have the small amount in the bottom, just above the intake, jets exposed, turn the jets to full, air off and see if the pump will shoot the water out of the jets with extreme force. Mine will shot water 20 feet away!!!! lol. If you don't have really good pressure, you may have a warn pump impeller. They can be damaged over time by chlorine based sanitizer, I never use chlorine, just bromine based shock etc.
The other item to check is if you have the right filter for your unit. Filters come in so many styles and densities. You may need to find one that allows better flow.
Assuming you find the root cause of your problem, good housekeeping, keeping as much contaminates as possible out of your tub will help. Very clean bathing suits or none at all,(yahoo) no body cosmetics such as body oils, moisturizers, perfumes etc. Keep chemical treatments to a minimum. Do a quick check weekly for PH, Total alkalinity, and bromine level. Adjust them sparingly so not to overdo any chemicals. Once you get everything under control, maintaining it is very easy and quick. Good Luck
Adding a filter onto an HVAC unit that's not designed for one will almost certainly cause problems... definitely with efficiency, possibly mechanical problems as well. If your model does not have a built-in filter you would probably be better served by getting a standalone air filter.
However, many units do have at least a basic filter built-in, and you may be able to clean it or replace it. Typically they are on the input side of the unit, to remove any particles or debris before the air passes through the unit. If you have or can find a user's manual, check there for instructions. Or it may be obvious once you start looking. In the USA they are often large square filters that come in standard sizes and slide into the unit, but on a smaller model like a window unit it may be a non-standard size. I do not know anything about HVAC equipment in China.
Best Answer
Go for it. Your only worry should be too much filter resistance, but you have that potential problem now.
You could go for a washable filter as the first layer, then a MERV13 for the second layer. Or a disposable MERV6 or MERV8 as the first layer and MERV13 for the final. Expect to wash or replace the outer layer more often.
Your unit may have a sight glass indicating "filter replacement", if so watch it. If not, you could cobble in a manometer. Or experiment a bit with cardboard blocking the filter, and get a sense if you can hear the difference in pitch when the airflow is blocked.